The design of new systems is becoming increasingly complex because of reliance on high performance features requiring tight tolerances and more robustness to system variations, for example, in resonance and anti-resonance. Resonance is a phenomenon that occurs in different types of systems, including mechanical, electrical, and acoustic systems. Many industries, for example, the disk drive industry, rely on system component redesigns in order to handle the resonances in their systems because current disk drive servo systems are unstable in the presence of resonances.
In a disk drive, a servo system is typically used to position a head assembly relative to a disk in order to reproducibly read and write data onto a specific location of a disk. The industry trend is toward increasing data storage densities and decreasing data access times by packing data locations as close to one another as possible (i.e., increasing track density) and by faster positioning of head assemblies over the data locations (i.e., decreasing seek time). This, however, leads to problems with resonance that develops in servo systems having tight alignment tolerances. Mechanical resonances in servo systems are a result of complex vibration interactions in the disk drives. Whereas, electrical resonances and anti-resonances in channel transfer functions may be the result of transmission line taps.
For example, in a magnetic disk drive, a head is flown over the disk surface on a thin air bearing. Mechanical vibrations in the drive due to air turbulence may result in tracking (i.e., head positioning) errors, thereby limiting achievable storage densities or resulting in increased access times to allow for resonance to dampen out of the system.
Unmeasured variables may affect the operation of a drive and can cause variations in performance from unit-to-unit, as well as within a unit, during use of the drive. These variables may include, for examples: temperature, spindle bearing asperity, disk flutter induced non-repeatable run-out (NRRO), and variable repeatable run-out (RRO).
One solution for reducing track errors is to redesign disk drive components that contribute to system resonance. Resonance may be engineered out by, for examples: designing smaller head assemblies, redesigning drive enclosures and mounts, and using disk materials that reduce disk flutter. Mechanically engineering out resonances, however, may be expensive and may delay getting a product to market.
Another solution is to design a servo control system so that the bandwidth of the system is increased and the resonant frequency is close to or inside the bandwidth of the system. The system bandwidth can be generally described as the range of frequencies within which a system will respond satisfactorily with acceptable gain and phase response. The gain margin and the phase response are measures of the relative stability of a system. The phase response of a system changes rapidly near resonance. As such, increasing the system's bandwidth and moving the resonant frequency nearer to a system's cross-over frequency makes the servo system more sensitive to the gain and phase response of the resonance.
One problem with these prior art servo systems is that as the system's bandwidth is increased, the performance of the system degrades due to unit-to-unit manufacturing variations as well as variations within a particular unit operated under different conditions. The performance of a system may be defined, for example, in terms of root mean square (rms) in servo tracking errors as a response to given vibrations, measurement noise, and run-outs. As such, a resulting high bandwidth control system will have less robustness (i.e., less gain and phase margin).
Another problem with prior solutions is that a large uncertainty results when attempting to design only a fixed disk drive control system using only one model that accounts for all system variations. A single controller that has to handle all the variations without adapting requires high robustness to large uncertainty in the control design models. Large model uncertainty leads to poorer achievable performance because the design has to achieve that performance over a much larger set of models. Therefore, a single controller has to sacrifice performance to achieve robustness.
As an example, it is difficult to predict structural frequencies of disk drive components using simulation models as unit-to-unit variations dominate variations in responses. In addition, the parameter estimation schemes used in prior art solutions have difficulty in accurately determining resonant modes in the presence of unmeasured stochastic and periodic disturbances with limited closed loop data. As such, the phase variations in the resulting transfer function of the drive control system are large, requiring high phase and gain margins nearing resonance. Furthermore, in-use variations such as those due to temperature and external vibrations create even more uncertainty. A larger uncertainty in the models used in control system design results in a lower performance in actual operation of the disk drive.
As such, prior art solutions that do not adapt to the changes caused by unmeasured variables are limited by the accuracy of one control model of a system, and do not allow for increased control performance based on resource utilization at design and manufacturing time. Although, conventional parameter adaptive schemes, for examples: Model Reference Adaptive Control (MRAC), Self-Tuning Regulator (STR), and Pole-Placement, may be effective in low bandwidth, low noise systems, these methods have significant in-use robustness problems in higher bandwidth systems (e.g., disk drive servo control systems). Adaptation to changes caused by unmeasured variables in resonant systems with such prior art methods is non-robust because prior art adaptive methods: 1) do not account for uncertainty in models; 2) attempt to handle adaptation to large in-use and unit-to-unit variations ignoring model uncertainty; and 3) do not attempt to match compute resource utilization with information that is available at design and manufacturing time.